Sir Graham Brady, who chairs the Tory committee that organises such votes, is expected to announce the move shortly.
Speculation about a possible vote this week has been mounting, as Mr Johnson continues to face calls to resign over lockdown parties.
A no-confidence vote will be triggered if 54 Tory MPs submit letters of no-confidence in him.
Former minister Jesse Norman is the latest to confirm he has done this.
In a letter to Mr Johnson posted on social media, Mr Norman, the MP for Hereford and South Herefordshire, said the PM had presided over “a culture of casual law-breaking” in No 10.
On Sunday the prime minister would not lose a confidence vote among his own MPs.
In the 10 days since MPs returned to their constituencies for the half term break, speculation has swirled about whether Mr Johnson will face an internal electoral battle to save his premiership.
For a confidence ballot to be triggered, 54 Tory MPs must formally put in a letter to Sir Graham Brady, the chairman of the 1922 Committee of backbench MPs, asking for one.
So far 28 Conservative MPs have publicly called on Boris Johnson to step down.
On Sunday, both Mr Shapps and Mr Scully shrugged off crowds booing the PM at the Jubilee thanksgiving service, with Mr Shapps saying politicians didn’t expect to be “popular all the time”.
Mr Scully told Channel 4’s The Andrew Neil Show politicians had been “booed through time immemorial”.
He added: “We may well have a vote of confidence. If it does happen, the prime minister, I know, will face it down.
“But whatever happens, we’ve got to get back to governing, to tackle the things that people want us to do on a day-to-day basis, not continuing… to look back at two years previous.
